Spanning 2-Connected Subgraphs in Alphabet Graphs, Special Classes of Grid Graphs
A.N.M. Salman, Hajo J. Broersma, Edy Tri Baskoro · Journal of automata, languages and combinatorics · 2003
A grid graph $G$ is a finite induced subgraph of the infinite 2-dimensional grid defined by $Z\times Z$ and all edges between pairs of vertices from $Z\times Z$ at Euclidean distance precisely 1. A natural drawing of $G$ is obtained by drawing its vertices in $R^2$ according to their coordinates. Apart from the outer face, all (inner) faces with area exceeding one (not bounded by a 4-cycle) in a natural drawing of $G$ are called the holes of $G$. We define 26 classes of grid graphs called alphabet graphs, with no or a few holes. We determine which of the alphabet graphs contain a Hamilton cycle, Le. a cycle containing all vertices, and solve the problem of determining a spanning 2-connected subgraph with as few edges as possible for all alphabet graphs.